Heat exchangers (LMTD) worksheet with answers

Free printable Heat exchangers (LMTD) worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
lengthT80 °C65 °C65 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 80 to 65 °C while the cold fluid heats from 15 to 65 °C. Find the log-mean temperature difference ΔTlm.

Th: 80 → 65 °CTc: 15 → 65 °C
ΔTlm = K
2.Easy
lengthT90 °C40 °C65 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 90 to 40 °C while the cold fluid heats from 25 to 65 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 40 °CTc: 25 → 65 °C
ΔTlm = K
3.Medium
lengthT130 °C75 °C25 °C45 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 400 kW. The hot fluid cools from 130 to 75 °C and the cold fluid heats from 25 to 45 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 400 kWU = 1000 W/(m²·K)Th: 130 → 75 °CTc: 25 → 45 °C
A = m²
4.Medium
lengthT170 °C60 °C70 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 110 kW. The hot fluid cools from 170 to 60 °C and the cold fluid heats from 15 to 70 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 110 kWU = 200 W/(m²·K)Th: 170 → 60 °CTc: 15 → 70 °C
A = m²
5.Hard
lengthT110 °C25 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 110 °C on the outside of the tubes of a condenser with a heat transfer area of 2.5 m² and U = 3000 W/(m²·K). Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 25 °C. Find the water outlet temperature Tc,out.

Ts = 110 °CA = 2.5 m²U = 3000 W/(m²·K)ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
6.Hard
lengthT150 °C105 °C25.07 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 150 to 105 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 150 → 105 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 29.07 K
  2. 2. ΔTlm = 19.58 K
  3. 3. A = 6.681 m²
  4. 4. A = 7.985 m²
  5. 5. Tc,out = 84.3 °C
  6. 6. A = 0.8647 m²

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